Abstract

Paying strict attention to Brandon Carter's several published renditions of anthropic reasoning, we present a ``nutshell'' version of the Doomsday argument that is truer to Carter's principles than the standard balls-and-urns or otherwise ``naive Bayesian'' versions that proliferate in the literature. At modest cost in terms of complication, the argument avoids commitment to many of the half-truths that have inspired so many to rise up against other toy versions, never adopting posterior outside of the convex hull of one's prior distribution over the ``true chance'' of Doom. The hyper-pessimistic position of the standard balls-and-urn presentation and the hyper-optimistic position of naive self-indicators are seen to arise from dubiously extreme prior distributions, leaving room for a more satisfying and plausible intermediate solution.